Estimating Turbulent Dissipation of Interacting Internal Waves Using Wave Kinetic Equation

The oceanic internal gravity wave (IGW) field is energized at large scales by atmospheric and tidal forcings and dissipated at small scales. Energy transfer across scales through interacting internal waves shapes the IGW spectra and facilitates turbulent dissipation for ocean mixing. The wave kinetic equation (WKE), which describes the evolution of a wave spectrum subject to triad interactions, is used to estimate this energy transfer and the resulting turbulent dissipation. Results show that the estimated turbulent dissipation is within a factor of 1.5 of the empirical formula of finescale parametrization across various IGW spectra that we assume as variations of the Garrett-Munk (GM) model. Most contributions come from parametric subharmonic instability (PSI) and local interactions. Induced diffusion only plays a role when the vertical-wavenumber spectrum significantly differs from the frequency spectrum. Incorporating tidal peaks into the IGW spectra moderately modifies the frequency cascade but does not significantly increase turbulent dissipation, aligning with finescale parametrization predictions, as low-mode tides contribute minimally to the total shear variance. Enhancing the inertial peaks, which are likely underestimated in GM models, results in reduced turbulent dissipation due to the suppression of both PSI and local interactions. This study provides a comprehensive, process-based framework for understanding ocean mixing under varying IGW spectra and realistic forcing conditions.